Write the prime factorization of 500 using exponents.

4. The cost of a new house is being reduced 22%

olganol [36]

1. Ok so first I would find 22% of 212,000 to do that you do: 22 divide 100 = 0.22

2. Now that you’ve turned 22% into a decimal as 0.22 you find what 22% of 212,000 is like so: 0.22x212,000 =46,640

3. Now that you have to reduce 212,000 but 22% to do this you just subtract: 212,000-46,640= 165,360

They would purchase the house for $165,360

3 0

3 years ago

You are considering developing a regression equation relating a dependent variable to two independent variables. One of the vari

lys-0071 [83]

Answer:

Step-by-step explanation:

a. How many dummy variables are needed to represent the categorical variable?

We need 1 less dummy variable than outcomes for the categorical variable.

categorical variable has 2 outcomes

So, we need 2-1 = 1 dummy variable.

Answer: 1

Note: If our categorical variable had 5 outcomes, we would need 5-1 = 4 dummy variables.

b. Write the multiple regression equation relating the dependent variable to the independent variables.

Note: Depending your your professor, this can be written one of the following ways...

yhat = a + b1 x1 + bx2

yhat = b0 + b1 x1 + b2 x2

yhat = beta0hat + beta1hat x1 + betahat2 x2

where x1 is the ratio variable

and x2 is the dummy variable

c. Interpret the meaning of the coefficients in the regression equation.

b0 = the predicted value of y when x1 and x2 both equal 0.

b1 = the change in y when x1 increases by 1 unit holding x2 constant.

b2 = the predicted difference in y between the two possible outcomes of the categorical variable holding x1 constant.

7 0

3 years ago

A biologist is studying the elk population in a county park. She starts with only 2 elk and observes that the number of elk trip

DochEvi [55]

Answer:

The expression that represents the population of elk is: $\text{elk}(t) = 2*3^t$ . It'll take 6 years for the population to reach 1,458 individuals.

Step-by-step explanation:

Since the number of elks triples every year and starts at $\text{elk}(0) = 2$ , then after the first year the population will be:

$\text{elk}(1) = \text{elk}(0)*3 = 2*3$

While on the second year, it'll be:

$\text{elk}(2) = \text{elk}(1)*3 = 2*3*3 = 2*3^2$

On the third year:

$\text{elk}(3) = \text{elk}(2)*3 = 2*3^2*3 = 2*3^3$

And so on, therefore the expression that describes the population of elk as the years passes is:

$\text{elk}(t) = 2*3^t$

If we want to know the number of years until the population reach 1,458 elk, we need to apply this value to the left side of the equation and solve for t.

$1458 = 2*3^t\\3^t = \frac{1458}{2}\\3^t = 729\\ln(3^t) = ln(729)\\t*ln(3) = ln(729)\\t = \frac{ln(729)}{ln(3)} = 6$